Adventure Time (Season 1)
So Season 1 doesn't really have much rhyme or reason to the way it's arranged (it's there, but ignorable, I should say), and is focused on basically establishing the identities of the main cast. So instead we're going to talk about the question presented: why do people like this show.
I mean, there's an easy, easy answer to that, but it hasn't happened yet.
So here's the impressions season 1 will send you away with, in roughly descending order of how present they are in the show and thus how likely they are to keep someone watching.
The animation is amazingly kinetic. There is ALWAYS a lot of motion going on at any given time, and the show's ability to project energy and draw the eye to something important going on is nearly unparalleled. There's relatedly also a lot of emotion from any character in a given scene, and a high willingness to bend or alter the characters and their models if that's what's needed in a given scene.
The show is constantly putting more into the show. More characters, new places, new genres, new things that don't quite make sense. But more importantly those things are very distinct, with a lot of personality. By way of comparison, let's take Tree Trunks and Spitfire, from FiM. I could actually tell you as much about Tree Trunks after her one feature episode as I could after, if memory serves, three from Spitfire. Which isn't a dig at the latter, she's a reasonably nuanced character given her actual story roles and probably has plenty of fans. Meanwhile I've definitely met some Adventure Time fans who really, really don't like Tree Trunks. But it's a difference in style, because the point of her episode is a character with all these foibles and quirks and how she impacts the heroes in about three different contexts within her one episode. The oddity with the show is that it has so many characters like this that over time the "main cast" ends up expanding from four (Finn, Jake, Bubblegum, Ice King) to what TV Tropes has listed as ten, of which I'd only quibble on one entry.
The show is unrepentantly geeky of course (most cartoons are if you scratch the surface, it's almost as though animators and artists are a core geekdom constituency) , but it's very specifically all about Dungeons and Dragons. Even setting aside the dungeon crawl episodes, there's a very d20 vibe about how our heroes operate. I'm not going to dwell on this, being only peripherally aware of the subject matter, but it's really noticeable.
Something is off about the world of Ooo. It's openly post-apocalyptic while also having a neo-medieval vibe, but that's obvious from the opening credits. Even without that, the surface normality of Finn and how it contrasts not just with the existence but with the sheer VARIETY of perils and mutants and monsters in the world suggest something very wrong has happened, but it's so normalized for the characters you can only see it along the edges.
Other thoughts... I remember the first time I watched this season thinking that it was some sort of sociological experiment. It's structurally laid out like a kid's show (11 minute format aside), and has applicable life lessons as often as not, but the path from A to B is so bizarre that it's like they're trying to stealth teach the aesops. This aspect is still there, but with the benefit of watching later I'm starting to think the series bible had to include elements of season 4, but their ability to reuse earlier elements means that it's easy to mix up with stuff they just watched the fans and brought back later because they were liked.
Best Episode: Henchman. The last five episodes of the season are all worthy in their own way, so I'm just tiebreaking for the one with Marceline. I know, boring, sorry.
Weakest Episode: Prisoners of Love. This episode is trying to just be this generalized introduction for the Ice King, but it also means most of the episode is just princesses whining at Finn. About as dry and long as an 11 minute cartoon can be I think.
Rating: 6/10. I don't really get into the season flow much in this writeup, but most of the first half of the season is pretty eh. Probably the show's biggest strength is showing established elements in new contexts and well, there wasn't anything established for most of this season.